[superprismatic]

On a TV stunt show, a couple is given the

sequence of numbers 8,7,2,1,4,10,6,11,12,9,3,5

and required to straighten them out in the

following way. The husband is to interchange

pairs of numbers, never touching the same

number twice. His wife is then to take the

sequence her husband leaves and also make

interchanges of numbers, again without touching

the same number twice. When she finishes, the

numbers are to be in order from 1 to 12. The

husband begins by switching 1 and 8; how

should he continue?

SUPERPRISMATIC NOTE: No information is either

provided or implied about the number of swaps

each makes. Also, "Touching" a number means

using it in a swap. When the wife's turn begins,

she is allowed to touch any or all of the numbers

of the sequence she inherits from her husband's

turn, but no more than once each.

[Guest]

quote name='superprismatic' date='03 August 2009 - 03:30 PM' timestamp='1249331439' post='191776']

On a TV stunt show, a couple is given the

sequence of numbers 8,7,2,1,4,10,6,11,12,9,3,5

and required to straighten them out in the

following way. The husband is to interchange

pairs of numbers, never touching the same

number twice. His wife is then to take the

sequence her husband leaves and also make

interchanges of numbers, again without touching

the same number twice. When she finishes, the

numbers are to be in order from 1 to 12. The

husband begins by switching 1 and 8; how

should he continue?

SUPERPRISMATIC NOTE: No information is either

provided or implied about the number of swaps

each makes. Also, "Touching" a number means

using it in a swap. When the wife's turn begins,

she is allowed to touch any or all of the numbers

of the sequence she inherits from her husband's

turn, but no more than once each.

[Guest]

Husband then swaps (7,9),(2,12),(4,11),(10,6),(3,5)

Then Wife swaps (2,9),(3,12),(4,8),(5,11),(7,10)

[Guest]

The husband should leave 1, 9, 12, 8, 11, 6, 10, 4, 2, 7, 5, 3.

[Guest]

Husband: 1x8, 7x9, 12x2, 11x4, 6x10, 5x3 leaving 1 9 12 8 11 6 10 4 2 7 5 3

Wife: 2x9, 3x12, 4x8, 5x11, 10x7 leaving 1 2 3 4 5 6 7 8 9 10 11 12

You can start with any number putting it in the correct place...

For example: original series: 8,7,2,1,4,10,6,11,12,9,3,5. I will start putting 4 in the correct place so:

Me: 1x4,5x8,7x6,2x10,11x12,3x9 leaving 5 6 10 4 1 2 7 12 11 3 9 8

My wife: 1x5,2x6,3x10,8x12,9x11 leaving 1 2 3 4 5 6 7 8 9 10 11 12

The trick is always follow the number you carry from the first position. In SUPERPRISMATIC case you have to follow the 8 that falls in position 4. Therefore you have to put 4 in 8th position and so on